In a large bowl, whisk together the gluten-free flour, sugar, baking powder, salt, and yeast. Make sure the yeast is evenly distributed.
In a separate bowl, whisk together the warm milk, melted butter, and eggs until well combined.
Pour the wet ingredients into the dry ingredients and mix with a wooden spoon or stand mixer with a dough hook until a smooth, slightly sticky dough forms. It will be wetter than traditional wheat dough.
Grease a 9x5 inch loaf pan and set aside. Cover the bowl with plastic wrap and let the dough rise in a warm place for about 1 hour, or until doubled in size.
While the dough is rising, prepare the cinnamon swirl filling by creaming together the softened butter, brown sugar, and cinnamon until a paste forms.
Once the dough has risen, punch it down gently. Turn the dough out onto a lightly floured surface and roll it into a rectangle approximately 10x15 inches.
Spread the cinnamon swirl filling evenly over the rolled-out dough, leaving a small border.
Starting from one of the long sides, tightly roll up the dough into a log. Pinch the seam to seal.
Carefully transfer the rolled dough seam-side down into the prepared loaf pan.
Cover the loaf pan loosely with plastic wrap and let it rise in a warm place for another 30-45 minutes, or until it has risen slightly above the rim of the pan.
Preheat your oven to 375°F (190°C).
Bake for 40-50 minutes, or until the bread is golden brown and sounds hollow when tapped on the bottom. If it starts to brown too quickly, loosely tent with foil.
Let the bread cool in the pan for 10-15 minutes before transferring it to a wire rack to cool completely.
Notes
Store cooled bread in an airtight container at room temperature for up to 3 days. Can be frozen for longer storage.